I think the confusion is that Leo does not mean lion. ライオン or しし is a lion. Leo is a constellation, which is called レオ or 獅子座（ししざ）
Ehh probably makes more sense the way you see it with being sick. I would only argue that 病気 shouldn’t be used here because it refers more to a disease rather than just having a cold. At least that is my understanding. I will update with 体調が悪くなりましたから明日仕事に行きません。Unless you have another suggestion that would make more sense/be easier to understand.
I would think that you could make a date the subject of the sentence. I think it really just depends on how you phrase it.
I think right now this reads like “I will not feel well tomorrow so I will not go to work.”
Maybe something like this would be better?
体調が悪くなりましたので明日仕事に行けません
I don’t feel well, so I won’t be able to go to work tomorrow.
The basic dictionary form or ます equivalent typically takes on a future meaning, so I think the first clause should be in past tense.
Great way to practice your Japanese! Good work 
This 80/20 guide is really helpful, I’m not a fan of grammar so the way he explains it makes it much easier! Thank you!
Interesring, but this was not about the omission of particles (which is mostly a thing in colloquial speech), but about using する instead of 浴びる. What does your language partner think about that?
Am I crazy or is the katakana in #1 & #4 really tiny?
I couldn’t say whether or not you’re crazy, but yeah, that’s half-width kana. Not completely sure how that could have been selected by accident.
Ok cool, wasn’t sure if it was just my laptop acting up or something. Thanks. 
Got me on that one. Completely forgot the past tense here. Will Update.
I was annoyed by the katakana switch, xd.